Why does the car shake at idle but not when accelerating?

[LeRebecca]

Common reasons for a car shaking at idle but not when accelerating include a dirty throttle body or excessive carbon buildup in the fuel injectors. When there is too much carbon buildup inside the engine, the gasoline sprayed by the cold-start fuel injector can be largely absorbed by the carbon deposits, resulting in an overly lean air-fuel mixture during cold starts and making it difficult to start the engine. In this situation, the engine will only start easily once the carbon deposits have absorbed enough gasoline to become saturated. After starting, the gasoline adsorbed on the carbon deposits will then be drawn into the combustion chamber by the engine's vacuum suction and burned. This causes the air-fuel mixture to fluctuate between lean and rich, leading to rough idling after a cold start. The lower the temperature, the more fuel is required for a cold start, and the presence of carbon deposits will have a greater impact on the cold-start process.